He accomplishes that a while ago when he becomes Lord Paramount of the Trident though. Strictly speaking, he had no reason to continue amassing Kingdoms, though I guess it does make him "greater."He already officially controls 2/7, and with Sansa he can make that 3. I'm just not sure he decides to stop at 3. 1 was already enough to make him one of the most powerful lords in the Seven Kingdoms (although, admittedly, the Riverlands have been so badly weakened, this could be a 'In Name Only' type of deal) 2 makes it even better, as now he has in the Vale one of the only untouched armies in the Seven Kingdoms (the other being Dorne).
As a side note, I think it's a bit premature to claim that The Game will become meaningless once The Others and/or Dragons show up. Daenerys and the dragons only represent another player, albeit a far more difficult one to deal with. The Others? If anything, I would think for someone like Littlefinger, they'd make it the best time to play. Afterall, with The Others bearing down on Westeros, who would possibly want to play The Game outside of Littlefinger? I'd almost find it far more likely that everyone else starts panicking over The Others and Littlefinger just takes advantage of it by being able to take crazy moves he could never pull off if everyone wasn't terrified.
That said, I don't expect Littlefinger to win. The most likely (and arguably most cliche) ending would be for Sansa to turn on him and beat him at his own game, since she is arguably his only weakness at this point. Second to that, I could see him looking at say, Daenerys's army and realizing that his fun is up, and joining up with her and starting a new round of The Game from within her rule. Whether someone like Varys would actually allow this to happen is another matter all together, but presumably Littlefinger would also be aware of this. If he switches sides over to Daenerys, she might be more than happy to let him keep some, or even all, of the Kingdoms he acquired - they had all been held by helpers of the Usurper after all!
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xp1337: Don't you wish there was a spell-checker that told you when you a word out?
GotD (219/384) Melee v FFX